http://cs224w.stanford.edu Observations Models Algorithms Small - PowerPoint PPT Presentation

CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University http://cs224w.stanford.edu

Observations Models Algorithms Small diameter, Erdös-Renyi model, Decentralized search Edge clustering Small-world model Patterns of signed Structural balance, Models for predicting edge creation Theory of status edge signs Viral Marketing, Blogosphere, Independent cascade model, Influence maximization, Memetracking Game theoretic model Outbreak detection, LIM Preferential attachment, PageRank, Hubs and Scale-Free Copying model authorities Densification power law, Link prediction, Microscopic model of Shrinking diameters Supervised random walks evolving networks Strength of weak ties, Community detection: Kronecker Graphs Core-periphery Girvan-Newman, Modularity 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2

 Networks with positive and - - negative relationships +  Our basic unit of investigation will be signed triangles - -  First we talk about undirected networks then directed  Plan for today: +  Model: Consider two soc. theories of signed nets  Data: Reason about them in large online networks  Application: Predict if A and B are linked with + or - 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3

 Networks with positive and negative relationships  Consider an undirected complete graph  Label each edge as either:  Positive : friendship, trust, positive sentiment, …  Negative : enemy, distrust, negative sentiment, …  Examine triples of connected nodes A, B, C 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4

 Start with the intuition [Heider ’46]:  Friend of my friend is my friend  Enemy of enemy is my friend  Enemy of friend is my enemy  Look at connected triples of nodes: + - + - - + - + - + - + Unbalanced Balanced Inconsistent with the “friend of a friend” Consistent with “friend of a friend” or or “enemy of the enemy” intuition “enemy of the enemy” intuition 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5

 Graph is balanced if every connected triple of nodes has:  All 3 edges labeled +, or  Exactly 1 edge labeled + Unbalanced Balanced 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6

 Balance implies global coalitions [Cartwright-Harary]  If all triangles are balanced , then either:  The network contains only positive edges, or  Nodes can be split into 2 sets where negative edges only point between the sets - + + + R L 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7

Every node in L is enemy of R – B D + – Any 2 nodes + Any 2 nodes + A in R are friends in L are friends – + R C E L Friends of A Enemies of A 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8

 International relations:  Positive edge: alliance  Negative edge: animosity  Separation of Bangladesh from Pakistan in 1971: U S supports P akistan. Why? B  USS R was enemy of C hina – –?  C hina was enemy of I ndia – P I  I ndia was enemy of P akistan + –  U S was friendly with C hina +? C +  C hina vetoed – B angladesh from U.N. U R 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 10

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 11

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 12

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 13

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 14

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 15

 So far we talked about complete graphs Def 1: Local view Fill in the missing edges to achieve balance - - Def 2: Global view + Divide the graph into - + two coalitions The 2 definitions are equivalent! Balanced? 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 16

 Graph is balanced if and only if it contains no cycle with an odd number of negative edges  How to compute this? –  Find connected components on + edges – – –  If we find a component of nodes on +edges Even length that contains a –edge ⇒ Unbalanced cycle  For each component create a super-node –  Connect components A and B if there is a – – negative edge between the members – –  Assign super-nodes to sides using BFS Odd length cycle 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 17

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 18

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 19

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 20

 Using BFS assign each node a side  Graph is unbalanced if any two super-nodes are assigned the same side L R R L L L  R Unbalanced! 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 21

10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 22

[CHI ‘10]  Each link A  B is explicitly tagged with a sign:  E pinions: Trust/Distrust  Does A trust B’s product reviews? + – – + (only positive links are visible) + – + – – +  W ikipedia: Support/Oppose – – + +  Does A support B to become + Wikipedia administrator?  S lashdot: Friend/Foe  Does A like B’s comments?  Other examples:  Online multiplayer games 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 23

[CHI ‘10]  Does structural balance hold? + + – x –  Compare frequencies of signed triads + + + – in real and “shuffled” data x + + Epinions Wikipedia + + Triad Balance + P(T) P 0 (T) P(T) P 0 (T)  + Real data + Balanced 0.87 0.62 0.70 0.49 + + -  + - 0.07 0.05 0.21 0.10 x + x – + Unbalanced +  + + + 0.05 0.32 0.08 0.49 + – - + x x –  - - + 0.007 0.003 0.011 0.010 + x - + P(T) … fraction of a triads P 0 (T)… triad fraction if the signs would be random Shuffled data 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 24

 Intuitive picture of social network in terms of densely linked clusters  How does structure interact with links?  Embeddedness of link (A,B): Number of shared neighbors 25

[CHI ‘10] Epinions  Embeddedness of ties:  Positive ties tend to be more embedded  Positive ties tend to be more clumped together Wikipedia  Public display of signs (votes) in Wikipedia further attenuates this 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 26

[CHI ‘10]  Clustering: +  +net: More clustering than baseline + + - +  –net: Less clustering than baseline + - +  Size of max. component: + + - + +  +/–net: Smaller than the baseline 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 27

[CHI ‘10]      New setting: Links are directed and - + - +     created over time - + - +     X ⋅ ⋅ + - + -     A B  How many  are now 16 signed directed triads ( in directed networks people explained by balance? traditionally applied balance by ignoring edge directions )  Only half (8 out of 16)  Is there a better explanation? Yes. Status. 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 28

[CHI ‘10]  Status in a network [Davis-Leinhardt ’68] +  A ⟶ B :: B has higher status than A  A ⟶ B :: B has lower status than A –  (Note the notion of status is now implicit)  Apply this principle transitively over paths – +  Can replace each A ⟶ B with A ⟵ B  Obtain an all-positive network with same status interpretation 10/9/2012 Jure Leskovec: How people evaluate each other in social media 29

[CHI ‘10] X - X + + - A B A B Balance: + Balance: + Status: – Status: – Status and balance give different predictions! 10/9/2012 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 30